A Stealth Bracket?

A friend asked me about the brackets in use as a recent backgammon tournament held in California. The tournament is a popular one, but has to be played in two days. The organizers cap entry in the main event at 64 players, though more would like to play. Even with the cap on entries, however, the play ran late on Sunday night. It was a double-elimination format, with a progressive consolation. My friend suggested that the tourney would play more quickly, and accommodate more entries, if it were changed to a main – consolation – last chance format with slightly shorter rounds.

Those changes would make for a shorter tourney. He’d break even on the format changes – the round saved by not giving the middle-bracket winner a second chance at the main title would be offset by the extra round needed to accommodate the extra players. But the shorter rounds would speed things up. There are various other ways to make the event play more quickly also.

The brackets that were actually played have a number of curious features. Perhaps this tourney has an example of a stealth bracket – a bracket intended to conceal some of its features.

Here is my redrawing of the brackets for the tourney: Stealth64. I’ve made a couple of changes so that I could get all three brackets, the winners’, the losers’, and the consolation, onto a single sheet so that it’s easier to see how they relate to each other. I have not changed anything else, however, leaving in place some very odd features.

I have a good deal of experience in looking at brackets, and can usually see what’s going on in a minute or two. But I found this format opaque. It was not until I’d spent more than an hour pouring over printouts that I saw what was happening. You’re invited to pause, now, and look at my redrawn bracket to see if you can do better.

The first thing that flummoxed me was that the match numbers were out of order. Everything I know about how to do the drops for a 64-player tourney so that there will be as few repeat pairings as possible was useless. So I initially wondered if the drops were well done.

As it happens, the drops are not awful. There are only two misplaced drops in the middle bracket, so there are two possible repeats that could be entirely avoided. As it happens, in the tourney as played, one of these two bad drops actually led to a repeat match. The drops into the third bracket are worse. There’s one very bad drop that could (but didn’t) lead to a repeat pairing in the very first round of the third bracket, and it should be possible to avoid most of the potential repeats in the third round.

So, there are some bad drops, and the unusual way the matches are numbered makes it hard to see them. But that’s not why I think this might be considered a stealth bracket.

Actually, there’s a plausible reason for the odd match numbering. The matches may be out of order, but the drops are in numerical order! I’ve never seen this done before, but you could argue that this makes the bracket easier to use – when entering names on the drop lines, you presumably know what match you’re coming from, so it’s not much of an advantage to have orderly match numbers. What you have to hunt for is the proper drop, and these may be easier to find when they’re in numerical order.

Look again, and find something else that’s peculiar.

It’s in the middle bracket. Instead of having rounds G, H, J, K, L, and M, the bracket has rounds G, G, H, J, J, and K! Why would anyone do that?

Look now at the third bracket. The two G rounds and the two J rounds both drop into the same round of the consolation. That’s the sneaky bit. By giving two rounds the same letter designation, the bracket is concealing the fact that two sets of drops are going to the same round, and that its happening twice. You have to consider the middle bracket and the third bracket together, or you won’t notice it.

I have no idea, of course, what was in the mind of the bracket designer. But the only reason I can think of to have duplicate G and J rounds is to make it harder to see that there are overlapping sets of drops in the consolation bracket.

Overlapping drops are inherently unfair. They match players with different records against each other, which is just what a progressive bracket is not supposed to do. We’ve already seen that the strange match numbering scheme tends to hide some bad drops. Are the duplicate rounds hiding some bad round overlaps?

No, not really. The round overlaps are not bad. As noted in my post on third brackets, they’re often pretty much unavoidable.

It would be possible to structure the bracket with fewer overlaps – I see two ways of doing that. But one of my alternative structures plays out in eight rounds, and the other in nine. The lower bracket actually used takes only seven rounds. Now, given that the first of those rounds can’t start until three rounds have been played in the brackets above it, it’s really a ten-round tourney. And ten rounds is what it takes to produce a winner from the two double-elimination brackets above it.

So, while it may be that the third bracket will play a little more quickly because those are shorter matches, I think it was an entirely reasonable choice to accept a little more round overlap in the cause of making sure that the tourney as a whole, which we already know is almost too long for the time available, finishes at a reasonable hour.

The duplicate round labels are not concealing a flaw in the design – in this respect, at least, the design is not flawed. But they are concealing a feature that, if they notice it, some people won’t like. And I sympathize with a director who takes a “what they don’t notice won’t hurt them” approach. I know that one of the things I really wouldn’t want to have to do towards the end of a long tournament, where everyone it tired and some tempers are a bit frayed, is to explain why the round overlap is an unfortunate necessity rather than an avoidable flaw.

Still, I’m not sure how I feel about the ethics of this. I see the appeal of burying the round overlap issue, but it goes against the grain to make brackets intentionally difficult to understand.